# Poisson Distribution

Hello All,

I am not sure how to solve this one. I would appreciate any thoughts.

A medical insurance company offers two deductible plans: high deductible plan with 1000 Euro annual premium/1000 Euro Deductible, and low deductible plan with 3000 Euro annual premium/250 Euro deductible. Moreover, it is assumed that medical claims require > 1000 Euro for medical payments. If we model the number of medical claims as a Poisson random variable with mean lambda (λ), when is the insurance plan with 1000 Euro deductible cheaper for the claimant on average?

I am not sure how to solve this. I would appreciate any thoughts.

Thanks

Where did you get this problem? Not from the CFA curriculum: it doesn’t cover Poisson distributions.

Nevertheless, we need to determine the value of λ that makes the costs of the two plans equal:

1,000 + 1,000λ = 3,000 + 250λ

750λ = 2,000

λ = 8/3

So, if the mean number of medical claims is less than 8/3, the first (1,000/1,000) plan is (on average) less expensive; if the mean number of medical claims is greater than 8/3, the second (3,000/250) plan is (on average) less expensive.

Thank you so much, S2000magician. I was reading an article on Binomial, Hypergeometric distribution from one of the stats books I borrowed from the library, and I came across this problem. Thanks again for your help. I truly appreciate it.

My pleasure.